A Robust Optimization Method for Systems With Significant Nonlinear Effects

1993 ◽  
Author(s):  
Jyh-Cheng Yu ◽  
Kosuke Ishii
Keyword(s):  
Heat Treatment ◽  
Robust Optimization ◽  
Nonlinear Effects ◽  
Optimization Method ◽  
Post Heat Treatment ◽  
Worst Case ◽  
Estimation Scheme ◽  
Optimization Methodology ◽  
Major Factors ◽  
The Cost

Abstract This paper describes a robust optimization methodology for design involving either complex simulations or actual experiments. The proposed procedure optimizes the worst case response that consists of a weighted sum of expected mean and response variance. The estimation scheme for expected mean and variance adopts the modified 3-point Gauss quadrature integration to assure superior accuracy for systems with significant nonlinear effects. We apply the proposed method to the robust design of geometric parameters of heat treated parts to minimize the cost of post heat treatment operations. The paper investigates the major factors influencing geometric distortions due to heat treatment and the rules of thumb in design. The study focuses on relating dimensional distortion to the design of part geometry. To illustrate the utility of the proposed method, we present the formulation of a case study on allocation of dimensions of preheat treated (green) shafts to minimize the cost of post heat treatment operations. The final result is not presented yet pending the completion of further experiments.

A Bi-Level Multi-Objective Robust Design Optimization Method With Multiple Robustness Index Capabilities

2011 ◽  
Author(s):  
Todd Letcher ◽  
M.-H. Herman Shen
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Method ◽  
Robust Design Optimization ◽  
Nsga Ii ◽  
Worst Case ◽  
Multi Objective ◽  
Robustness Index ◽  
Multiple Robustness

A multi-objective robust optimization framework that incorporates a robustness index for each objective has been developed in a bi-level approach. The top level of the framework consists of the standard optimization problem formulation with the addition of a robustness constraint. The bottom level uses the Worst Case Sensitivity Region (WCSR) concept previously developed to solve single objective robust optimization problems. In this framework, a separate robustness index for each objective allows the designer to choose the importance of each objective. The method is demonstrated on a commonly studied two-bar truss structural optimization problem. The results of the problem demonstrate the effectiveness and usefulness of the multiple robustness index capabilities added to this framework. A multi-objective genetic algorithm, NSGA-II, is used in both levels of the framework.

scholarly journals Robust Design of a Smart Structure under Manufacturing Uncertainty via Nonsmooth PDE-Constrained Optimization

2018 ◽  
Vol 885 ◽  
pp. 131-144
Author(s):  
Philip Kolvenbach ◽  
Stefan Ulbrich ◽  
Martin Krech ◽  
Peter Groche
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Smart Structure ◽  
Uncertain Parameters ◽  
Sensing Element ◽  
Sensor Element ◽  
Worst Case ◽  
Sqp Method ◽  
Nonsmooth Problems

We consider the problem of finding the optimal shape of a force-sensing element which is integrated into a tubular structure. The goal is to make the sensor element sensitive to specific forces and insensitive to other forces. The problem is stated as a PDE-constrained minimization program with both nonconvex objective and nonconvex constraints. The optimization problem depends on uncertain parameters, because the manufacturing process of the structures underlies uncertainty, which causes unwanted deviations in the sensory properties. In order to maintain the desired properties of the sensor element even in the presence of uncertainty, we apply a robust optimization method to solve the uncertain program.The objective and constraint functions are continuous but not differentiable with respect to the uncertain parameters, so that existing methods for robust optimization cannot be applied. Therefore, we consider the nonsmooth robust counterpart formulated in terms of the worst-case functions, and show that subgradients can be computed efficiently. We solve the problem with a BFGS--SQP method for nonsmooth problems recently proposed by Curtis, Mitchell and Overton.

scholarly journals Energy Curtailment Scheduling MILP Formulation for an Islanded Microgrid with High Penetration of Renewable Energy

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6038
Author(s):  
Woan-Ho Park ◽  
Hamza Abunima ◽  
Mark B. Glick ◽  
Yun-Su Kim
Keyword(s):  
Objective Function ◽  
Cost Minimization ◽  
Optimization Method ◽  
Time Interval ◽  
Specific Time ◽  
High Penetration ◽  
Optimization Methodology ◽  
The Cost ◽  
Pv Generation ◽  
Model Features

The efficiency of photovoltaic (PV) cells has improved significantly in the last decade, making PV generation a common feature of the sustainable microgrid. As the PV-powered microgrid reaches high penetrations of intermittent PV power, optimum scheduling of over-production is necessary to minimize energy curtailment. Failure to include an accurate assessment of curtailed energy costs in the scheduling process increases wasted energy. Moreover, applying an objective function without considering the cost coefficients results in an inefficient concentration of curtailed power in a specific time interval. In this study, we provide an optimization method for scheduling the microgrid assets to evenly distribute curtailment over the entire daily period of PV generation. Each of the curtailment intervals established in our optimization model features the application of different cost coefficients. In the final step, curtailment costs are added to the objective function. The proposed cost minimization algorithm preferentially selects intervals with low curtailment costs to prevent the curtailment from being concentrated at a specific time. By inducing even distribution of curtailment, this novel optimization methodology has the potential to improve the cost-effectiveness of the PV-powered microgrid

Risk-Based Robust Bidding Strategies for EVs’ Aggregators in Day-ahead Markets with Uncertainty

2020 ◽  
Author(s):  
Ahmed Abdelmoaty ◽  
Wessam Mesbah ◽  
Mohammad A. M. Abdel-Aal ◽  
Ali T. Alawami
Keyword(s):  
Robust Optimization ◽  
Electricity Market ◽  
Real Life ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Bidding Strategies ◽  
Wind Generators ◽  
Proposed Model ◽  
Optimal Bidding

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual<br>power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy<br>prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO's profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from<br>the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.<br>

Classification of the factors forming the cost of the web-site

2017 ◽  
Vol 31 (2) ◽  
pp. 82-89
Author(s):  
E. S. Epifanov
Keyword(s):  
Web Site ◽  
Internet Site ◽  
Advantages And Disadvantages ◽  
Major Factors ◽  
The Cost ◽  
The Web

This article presents a classification of major factors that shape the cost of Internet site. Also discusses the limitations in determining the objectives of the web site; advantages and disadvantages of different factors.

Effect of post-heat treatment on microstructure and mechanical properties of laser welded Al-Cu-Mg alloy

2021 ◽  
Vol 64 ◽  
pp. 620-632
Author(s):  
Alexander Malikov ◽  
Anatoly Orishich ◽  
Igor Vitoshkin ◽  
Evgeniy Karpov ◽  
Alexei Ancharov
Keyword(s):  
Mechanical Properties ◽  
Heat Treatment ◽  
Mg Alloy ◽  
Post Heat Treatment ◽  
Microstructure And Mechanical Properties

scholarly journals Robust Universal Inference

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 773
Author(s):  
Amichai Painsky ◽  
Meir Feder
Keyword(s):  
Robust Estimation ◽  
Minimax Estimator ◽  
Worst Case ◽  
Capacity Theory ◽  
Alternative Approach ◽  
True Model ◽  
Finite Set ◽  
Universal Prediction ◽  
Estimation Scheme

Learning and making inference from a finite set of samples are among the fundamental problems in science. In most popular applications, the paradigmatic approach is to seek a model that best explains the data. This approach has many desirable properties when the number of samples is large. However, in many practical setups, data acquisition is costly and only a limited number of samples is available. In this work, we study an alternative approach for this challenging setup. Our framework suggests that the role of the train-set is not to provide a single estimated model, which may be inaccurate due to the limited number of samples. Instead, we define a class of “reasonable” models. Then, the worst-case performance in the class is controlled by a minimax estimator with respect to it. Further, we introduce a robust estimation scheme that provides minimax guarantees, also for the case where the true model is not a member of the model class. Our results draw important connections to universal prediction, the redundancy-capacity theorem, and channel capacity theory. We demonstrate our suggested scheme in different setups, showing a significant improvement in worst-case performance over currently known alternatives.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

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